Both of my roadworthy R65's do the same thing, the '81 just had a transmission overhaul done 9,000 miles ago and still had the gear whine in third gear after the overhaul .
I've worked around jet aircraft for around 36 years, so my hearing is not great anymore, I don't notice any pronounced gear whine in fifth gear .
I've got 87,000 miles on the '81 and it has sounded the same since I got it .
One thing to check, if you can, is for water contamination of the transmission oil, if it has water in it, it looks like coffee with milk in it .
The water gets in by the rubber boot that covers up the speedometer drive cable where it enters the transmission .
If the boot looks deteriorated and not sealing well, good chance you have water in the transmission, pretty common problem .
You could use it as a 'bargaining tool' to negotiate a lower price .
Another quick things to look for, is gear oil dripping or on the rear wheel, quite common for o-rings to leak where the brake shaft goes through the final drive .
Take a good look at the brake master cylinder for leakage, quite common to get leakage here from a corroded and pitted cylinder bore, it's made from aluminum and if the brake fluid isn't flushed out regularly, damage happens here as well .
Malfunctioning odometer is another common problem, make sure it works, otherwise you may have a bike with unknown mileage .
The transmissions from the '81 model year, up to the end of the airhead series bikes, not quite sure when that was, but they are all interchangeable .